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x+4=2-1/3x
We move all terms to the left:
x+4-(2-1/3x)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
x-(-1/3x+2)+4=0
We get rid of parentheses
x+1/3x-2+4=0
We multiply all the terms by the denominator
x*3x-2*3x+4*3x+1=0
Wy multiply elements
3x^2-6x+12x+1=0
We add all the numbers together, and all the variables
3x^2+6x+1=0
a = 3; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·3·1
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{6}}{2*3}=\frac{-6-2\sqrt{6}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{6}}{2*3}=\frac{-6+2\sqrt{6}}{6} $
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